Tickets sold to a school dance cost $4 and the projected attendance is 300. for every $0.10 increase in price the attendance will decrease by 5. what ticket price will generate $1237.5?

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Answer 1 · 2016-08-08T19:08:38

$$4.50 or $5.50$

Attendance (A) given by:

$A = 300 - 5n$ where $n$ is every $0.10 over $4.

Ticket price (T) given by:

$T = 4 + 0.1n$

Total earnings (E) given by:

$E = A*T$

$E= (300-5n)(4+0.1n)$

$E = 1200 + 30n - 20n - 0.5n^2 = 1200 + 10n - 0.5n^2$

We want $E = 1237.5$ so

$1237.5 = 1200 + 10n - 0.5n^2$

Yielding a quadratic:

$0.5n^2 - 10n + 37.5 = 0$

Multiply by 2 to get tidier numbers. This is not really necessary, just out of preference.

$n^2 - 20n + 75 = 0$

Could easily factorise by eye but will use quadratic formula for completeness.

$n = (20+-sqrt((-20)^2 - 4(1)(75)))/2$

$n = (20+-sqrt(400 - 300))/2 = (20+-10)/2 = 15 or 5$

$n = 5 implies T = $4.50$

$n = 15 implies T = $5.50$